Dressians, Tropical Grassmannians, and Their Rays

Understand

The Dressian Dr(k,n) parametrizes all tropical linear spaces, and it carries a natural fan structure as a subfan of the secondaryfan of the hypersimplex \Delta(k,n).

• We explore the combinatorics of the rays of Dr(k,n), that is, the most degenerate tropical planes, for arbitrary k and n.
• This is related to a new rigidity concept for configurations of n-k points in the tropical (k-1)-torus.
• Additional conditions are given for k=3.